A Method for Assessing the Efficiency in Two-Stage Production Systems in the Presence of Dual-Role Factors

Due to the existence of dual-role factors, it is difficult to evaluate the production efficiency of two-stage systems. Unlike single-stage systems, two-stage systems involve intermediate products that serve as both inputs and outputs. Hence, to overcome existing obstacles, we propose a novel approach called the two-stage enhanced Russell model with dual-role factors (T-ERM-D) to assess the overall efficiency of two-stage production systems. Furthermore, divisional models are developed to evaluate the efficiency of each individual stage. The 0-1 programming is applied to deal with dual-role factors. To handle the non-linearity of these models, the Charnes-Cooper transformation is employed to convert them into linear ones. Using the proposed models, we evaluate efficiency scores of 10 supply chains involving suppliers and producers. By comparing the results obtained from new models with those obtained from models that do not consider dual-role factors, we validate the advantages of the proposed approach.